A time-optimal boundary controllability problem for the heat equation in a ball

2014 ◽  
Vol 144 (6) ◽  
pp. 1171-1189 ◽  
Author(s):  
Sorin Micu ◽  
Laurenţiu Emanuel Temereancă
Keyword(s):  
Optimal Control ◽  
Heat Equation ◽  
Parabolic Type ◽  
Time Optimal Control ◽  
Main Ingredient ◽  
Controllability Problem ◽  
Boundary Controllability ◽  
Müntz Polynomials ◽  
Time Optimal ◽  
Dimensional Ball

The aim of this paper is to study a boundary time-optimal control problem for the heat equation in a two-dimensional ball. The main ingredient is the extension of a result concerning Müntz polynomials due to Borwein and Erdélyi that allows us to prove an observability inequality for the dynamical system's truncation to a finite number of modes. This result, combined with a well-known Lebeau–Robbiano argument used to show the null-controllability of parabolic type equations, enables us to deduce the existence, uniqueness and bang-bang properties for the boundary time-optimal control.

scholarly journals Two-channel time-optimal control of nonstationary heat conductive process with account for response time of boundary control actions

2021 ◽  
Vol 29 (2) ◽  
pp. 47-60
Author(s):  
Natalya A. Il’ina
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Parabolic Type ◽  
Time Optimal Control ◽  
Optimal Time ◽  
Time Control ◽  
Distributed Parameters ◽  
Control Actions ◽  
Optimal Controllers ◽  
Time Optimal

The task of organization a closed time-optimal control system of linear object with distributed parameters of parabolic type is considered. The object has two lumped internal controls for the power of heat sources excited in the electromagnetic field of an inductor. The proposed method for the synthesis of optimal controllers uses an alternance method for calculating the optimal program controls for each of the control actions. An example of the construction of a quasi-optimal time control system for the process of periodic induction heating of a metal workpiece with constant values of the feedback coefficients calculated for the most characteristic initial spatial distribution is given.

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